Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture

Abstract

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulas which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices. The examples include the +-J and Gaussian Ising spin glasses on the square, hexagonal and triangular lattices, the Potts and Z_q models with chiral randomness on these lattices, and the three-dimensional +-J Ising spin glass and the random plaquette gauge model.

arXiv comment27 pages, 3 figures

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Cited by in corpus (26)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological fault-tolerance in cluster state quantum computation
• Towards Scalable Bosonic Quantum Error Correction
• Locations of multicritical points for spin glasses on regular lattices
• Multicritical points for the spin glass models on hierarchical lattices
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Multicritical point of Ising spin glasses on triangular and honeycomb lattices
• Error- and Loss-Tolerances of Surface Codes with General Lattice Structures
• Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Analytical evidence for the absence of spin glass transition on self-dual lattices
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
• Tailoring three-dimensional topological codes for biased noise
• Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
• Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model
• Duality analysis on random planar lattice
• The Random-Bond Ising Model and its dual in Hyperbolic Spaces
• Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory
• Properties of the multicritical point of +/- J Ising spin glasses on the square lattice
• Multicritical point of spin glasses
• The Implications of Ignorance for Quantum Error Correction Thresholds
• Multicritical Points of Potts Spin Glasses on the Triangular Lattice
• Phases of Floquet code under local decoherence
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions